H(·, ·)‐Cocoercive Operator and an Application for Solving Generalized Variational Inclusions | Zendy

Rais Ahmad | Zendy; Mohammad Dilshad | Zendy; Mu-Ming Wong | Zendy; Jen-Chin Yao | Zendy

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H(·, ·)‐Cocoercive Operator and an Application for Solving Generalized Variational Inclusions

Author(s) -

Rais Ahmad,

Mohammad Dilshad,

Mu-Ming Wong,

Jen-Chin Yao

Publication year - 2011

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2011/261534

Subject(s) - lipschitz continuity , mathematics , operator (biology) , convergence (economics) , resolvent , iterative method , monotone polygon , multiplication operator , mathematical analysis , algorithm , hilbert space , chemistry , geometry , biochemistry , repressor , transcription factor , economics , gene , economic growth

The purpose of this paper is to introduce a new H(⋅,⋅)-cocoercive operator, which generalizes many existing monotone operators. The resolvent operator associatedwith H(⋅,⋅)-cocoercive operator is defined, and its Lipschitz continuity is presented. By using techniques of resolvent operator, a new iterative algorithm for solving generalized variational inclusions is constructed. Under some suitable conditions, we prove the convergence of iterative sequences generated by the algorithm. For illustration, some examples are given

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